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It should be able to... I have a P4 2.66 here at work that's 24/7, 100%.... I've never had an ounce of problems with it..... I don't even hear it at full load....
Like OSU said, you should be just fine. I've had numerous stock IBM rigs at work over the last 2 years that have performed admirably using just the stock cooling.
My p4 1.4a in my sig is using dell's stock cooling, which is just a passive heatsink. I just have a fan sitting on top of it for insurance and it has not cause any problems.
My dell 5100 2.4P4 has been fine as well. Course I've modified it some for better air intake, and the lappy in general gets pretty hot, but I've had zero instability. About 23 minutes a frame on QMD's.
Dell Optiplex GX280 with a 2.8 Ghz Preshott that is on 30 days of uptime with 24/7 folding. The damn thing is somewhat loud but it beats the hell out of the fan spinning up and down every time you load an app. Sure, I think the air being exhausted out the back is hot enough to pop popcorn, but that's the damn Preshott's fault.
For an answer to your question, as long as ambient temps are not high, you should not have any problems with it. If Dell can't design a cooling system that allows the processor to run at full load under reasonable conditions, then I would send the damn thing back for a system that does since it would be a manufacturer's defect for not having a product that cannot do what it's supposed to be able to do.